;
; waverecon.pro - Reconstructs a wave transform.
;
; Copyright (C) 2005, 2006 Patricio Rojo
;
; This program is free software; you can redistribute it and/or
; modify it under the terms of the GNU General Public License
; as published by the Free Software Foundation; either version 2
; of the License, or (at your option) any later version.
;
; This program is distributed in the hope that it will be useful,
; but WITHOUT ANY WARRANTY; without even the implied warranty of
; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
; GNU General Public License for more details.
;
; You should have received a copy of the GNU General Public License
; along with this program; if not, write to the Free Software
; Foundation, Inc., 51 Franklin Street, Fifth Floor, 
;                   Boston, MA 02110-1301, USA.
;

;+
; NAME:
;	WAVERECON
;
; PURPOSE:
;	This function does an inverse wavelet transform
;
; CATEGORY:
;	Pato's Array Data Reduction Potpourri.
;
; CALLING SEQUENCE:
;
;	Result = WAVERECON(Wavelet, Dt, Scale, Cdelta, Psi0)
;
; INPUTS:
;       Wavelet: Complex two dimensional array containing the wavelet
;       Dt:      X axis sampling distance
;       Scale:   Vector of scale indices
;       Cdelta:  Wavelet reconstruction factor.
;       Psi0:    Wavelet parameter
;
; KEYWORD PARAMETERS:
;       DJ:     Spacing betweeen discrete scales. Default is 1/8.
;
; OUTPUTS:
;	This function returns the reconstructed array
;
; SIDE EFFECTS:
;
; RESTRICTIONS:
;
; PROCEDURE:
;	It just applies equation [11] of 
;            Torrence, C. and G. P. Compo, 1998: A Practical Guide to
;            Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78.
;
; EXAMPLE:
;	Reconstruct wavelet 'wave' that was created by Morlet mother
;	with standard parameters
;
;	  unwave = WAVERECON(wave, 1, scale, 0.776, !PI^(-0.25))
;
; MODIFICATION HISTORY:
; 	Written by:	Pato Rojo, Cornell.  Jul 2005 - Mar 2006
;			pato@astro.cornell.edu
;       strongly based on routine wavelet.pro (copyright (C)
;         1995-1998, Christopher Torrence and Gilbert P. Compo) 
;-

FUNCTION waverecon,w,dt,scale,cdelta,psi0,dj=dj

IF (N_ELEMENTS(dj) LT 1) THEN dj = 1./8

IF (cdelta EQ -1) THEN BEGIN
    y1 = -1
    MESSAGE,/INFO, $
      'cdelta undefined, cannot reconstruct with this wavelet'
ENDIF ELSE BEGIN
    y1=dj*sqrt(dt)/(cdelta*psi0)*(float(w) # (1./sqrt(scale)))
ENDELSE

RETURN,y1

END